/****************************************************************************
 *
 * Copyright 2016 Samsung Electronics All Rights Reserved.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing,
 * software distributed under the License is distributed on an
 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND,
 * either express or implied. See the License for the specific
 * language governing permissions and limitations under the License.
 *
 ****************************************************************************/
/****************************************************************************
 * libc/stdio/lib_dtoa.c
 *
 * This file was ported to NuttX by Yolande Cates.
 *
 * Copyright (c) 1990, 1993
 *      The Regents of the University of California.  All rights reserved.
 *
 * This code is derived from software contributed to Berkeley by
 * Chris Torek.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *      This product includes software developed by the University of
 *      California, Berkeley and its contributors.
 * 4. Neither the name of the University nor the names of its contributors
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 ****************************************************************************/

/****************************************************************************
 * Included Files
 ****************************************************************************/

#include <tinyara/config.h>

#include <stdint.h>
#include <string.h>

#include "lib_internal.h"

/****************************************************************************
 * Pre-processor Definitions
 ****************************************************************************/

#ifdef Unsigned_Shifts
#define Sign_Extend(a, b) if (b < 0) a |= 0xffff0000;
#else
#define Sign_Extend(a, b)		/* no-op */
#endif

#ifdef CONFIG_ENDIAN_BIG
#define word0(x) ((uint32_t *)&x)[0]
#define word1(x) ((uint32_t *)&x)[1]
#else
#define word0(x) ((uint32_t *)&x)[1]
#define word1(x) ((uint32_t *)&x)[0]
#endif

#ifdef CONFIG_ENDIAN_BIG
#define Storeinc(a, b, c) (((unsigned short *)a)[0] = (unsigned short)b, \
						   ((unsigned short *)a)[1] = (unsigned short)c, a++)
#else
#define Storeinc(a, b, c) (((unsigned short *)a)[1] = (unsigned short)b, \
						   ((unsigned short *)a)[0] = (unsigned short)c, a++)
#endif

#define Exp_shift  20
#define Exp_shift1 20
#define Exp_msk1    0x100000
#define Exp_msk11   0x100000
#define Exp_mask  0x7ff00000
#define P 53
#define Bias 1023
#define IEEE_Arith
#define Emin (-1022)
#define Exp_1  0x3ff00000
#define Exp_11 0x3ff00000
#define Ebits 11
#define Frac_mask  0xfffff
#define Frac_mask1 0xfffff
#define Ten_pmax 22
#define Bletch 0x10
#define Bndry_mask  0xfffff
#define Bndry_mask1 0xfffff
#define LSB 1
#define Sign_bit 0x80000000
#define Log2P 1
#define Tiny0 0
#define Tiny1 1
#define Quick_max 14
#define Int_max 14
#define Infinite(x) (word0(x) == 0x7ff00000)	/* sufficient test for here */

#define Kmax 15

#define Bcopy(x, y) memcpy((char *)&x->sign, (char *)&y->sign, \
						   y->wds*sizeof(long) + 2*sizeof(int))

/****************************************************************************
 * Private Type Definitions
 ****************************************************************************/

struct Bigint {
	struct Bigint *next;
	int k;
	int maxwds;
	int sign;
	int wds;
	unsigned long x[1];
};

typedef struct Bigint Bigint;

/****************************************************************************
 * Private Data
 ****************************************************************************/

static Bigint *freelist[Kmax + 1];

/****************************************************************************
 * Private Functions
 ****************************************************************************/

static Bigint *Balloc(int k)
{
	int x;
	Bigint *rv;

	if ((rv = freelist[k])) {
		freelist[k] = rv->next;
	} else {
		x = 1 << k;
		rv = (Bigint *)lib_malloc(sizeof(Bigint) + (x - 1) * sizeof(long));
		rv->k = k;
		rv->maxwds = x;
	}

	rv->sign = rv->wds = 0;
	return rv;
}

static void Bfree(Bigint *v)
{
	if (v) {
		v->next = freelist[v->k];
		freelist[v->k] = v;
	}
}

/* multiply by m and add a */

static Bigint *multadd(Bigint *b, int m, int a)
{
	int i, wds;
	unsigned long *x, y;
#ifdef Pack_32
	unsigned long xi, z;
#endif
	Bigint *b1;

	wds = b->wds;
	x = b->x;
	i = 0;
	do {
#ifdef Pack_32
		xi = *x;
		y = (xi & 0xffff) * m + a;
		z = (xi >> 16) * m + (y >> 16);
		a = (int)(z >> 16);
		*x++ = (z << 16) + (y & 0xffff);
#else
		y = *x * m + a;
		a = (int)(y >> 16);
		*x++ = y & 0xffff;
#endif
	} while (++i < wds);

	if (a) {
		if (wds >= b->maxwds) {
			b1 = Balloc(b->k + 1);
			Bcopy(b1, b);
			Bfree(b);
			b = b1;
		}
		b->x[wds++] = a;
		b->wds = wds;
	}

	return b;
}

static int hi0bits(unsigned long x)
{
	int k = 0;

	if (!(x & 0xffff0000)) {
		k = 16;
		x <<= 16;
	}

	if (!(x & 0xff000000)) {
		k += 8;
		x <<= 8;
	}

	if (!(x & 0xf0000000)) {
		k += 4;
		x <<= 4;
	}

	if (!(x & 0xc0000000)) {
		k += 2;
		x <<= 2;
	}

	if (!(x & 0x80000000)) {
		k++;
		if (!(x & 0x40000000)) {
			return 32;
		}
	}

	return k;
}

static int lo0bits(unsigned long *y)
{
	int k;
	unsigned long x = *y;

	if (x & 7) {
		if (x & 1) {
			return 0;
		}

		if (x & 2) {
			*y = x >> 1;
			return 1;
		}

		*y = x >> 2;
		return 2;
	}

	k = 0;
	if (!(x & 0xffff)) {
		k = 16;
		x >>= 16;
	}

	if (!(x & 0xff)) {
		k += 8;
		x >>= 8;
	}

	if (!(x & 0xf)) {
		k += 4;
		x >>= 4;
	}

	if (!(x & 0x3)) {
		k += 2;
		x >>= 2;
	}

	if (!(x & 1)) {
		k++;
		x >>= 1;
		if (!(x & 1)) {
			return 32;
		}
	}

	*y = x;
	return k;
}

static Bigint *i2b(int i)
{
	Bigint *b;

	b = Balloc(1);
	b->x[0] = i;
	b->wds = 1;
	return b;
}

static Bigint *mult(Bigint *a, Bigint *b)
{
	Bigint *c;
	int k, wa, wb, wc;
	unsigned long carry, y, z;
	unsigned long *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
#ifdef Pack_32
	uint32_t z2;
#endif

	if (a->wds < b->wds) {
		c = a;
		a = b;
		b = c;
	}

	k = a->k;
	wa = a->wds;
	wb = b->wds;
	wc = wa + wb;
	if (wc > a->maxwds) {
		k++;
	}

	c = Balloc(k);
	for (x = c->x, xa = x + wc; x < xa; x++) {
		*x = 0;
	}

	xa = a->x;
	xae = xa + wa;
	xb = b->x;
	xbe = xb + wb;
	xc0 = c->x;
#ifdef Pack_32
	for (; xb < xbe; xb++, xc0++) {
		if ((y = *xb & 0xffff)) {
			x = xa;
			xc = xc0;
			carry = 0;
			do {
				z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
				carry = z >> 16;
				z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
				carry = z2 >> 16;
				Storeinc(xc, z2, z);
			} while (x < xae);

			*xc = carry;
		}

		if ((y = *xb >> 16)) {
			x = xa;
			xc = xc0;
			carry = 0;
			z2 = *xc;
			do {
				z = (*x & 0xffff) * y + (*xc >> 16) + carry;
				carry = z >> 16;
				Storeinc(xc, z, z2);
				z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
				carry = z2 >> 16;
			} while (x < xae);

			*xc = z2;
		}
	}
#else
	for (; xb < xbe; xc0++) {
		if ((y = *xb++)) {
			x = xa;
			xc = xc0;
			carry = 0;
			do {
				z = *x++ * y + *xc + carry;
				carry = z >> 16;
				*xc++ = z & 0xffff;
			} while (x < xae);

			*xc = carry;
		}
	}
#endif

	for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc);
	c->wds = wc;
	return c;
}

static Bigint *p5s;

static Bigint *pow5mult(Bigint *b, int k)
{
	Bigint *b1, *p5, *p51;
	int i;
	static int p05[3] = { 5, 25, 125 };

	if ((i = k & 3)) {
		b = multadd(b, p05[i - 1], 0);
	}

	if (!(k >>= 2)) {
		return b;
	}

	if (!(p5 = p5s)) {
		/* first time */
		p5 = p5s = i2b(625);
		p5->next = 0;
	}

	for (;;) {
		if (k & 1) {
			b1 = mult(b, p5);
			Bfree(b);
			b = b1;
		}

		if (!(k >>= 1)) {
			break;
		}

		if (!(p51 = p5->next)) {
			p51 = p5->next = mult(p5, p5);
			p51->next = 0;
		}

		p5 = p51;
	}

	return b;
}

static Bigint *lshift(Bigint *b, int k)
{
	int i, k1, n, n1;
	Bigint *b1;
	unsigned long *x, *x1, *xe, z;

#ifdef Pack_32
	n = k >> 5;
#else
	n = k >> 4;
#endif
	k1 = b->k;
	n1 = n + b->wds + 1;
	for (i = b->maxwds; n1 > i; i <<= 1) {
		k1++;
	}

	b1 = Balloc(k1);
	x1 = b1->x;
	for (i = 0; i < n; i++) {
		*x1++ = 0;
	}

	x = b->x;
	xe = x + b->wds;
#ifdef Pack_32
	if (k &= 0x1f) {
		k1 = 32 - k;
		z = 0;
		do {
			*x1++ = *x << k | z;
			z = *x++ >> k1;
		} while (x < xe);

		if ((*x1 = z)) {
			++n1;
		}
	}
#else
	if (k &= 0xf) {
		k1 = 16 - k;
		z = 0;
		do {
			*x1++ = ((*x << k) & 0xffff) | z;
			z = *x++ >> k1;
		} while (x < xe);

		if ((*x1 = z)) {
			++n1;
		}
	}
#endif
	else {
		do {
			*x1++ = *x++;
		} while (x < xe);
	}

	b1->wds = n1 - 1;
	Bfree(b);
	return b1;
}

static int cmp(Bigint *a, Bigint *b)
{
	unsigned long *xa, *xa0, *xb, *xb0;
	int i, j;

	i = a->wds;
	j = b->wds;
#ifdef CONFIG_DEBUG_LIB
	if (i > 1 && !a->x[i - 1]) {
		ldbg("cmp called with a->x[a->wds-1] == 0\n");
	}

	if (j > 1 && !b->x[j - 1]) {
		ldbg("cmp called with b->x[b->wds-1] == 0\n");
	}
#endif

	if (i -= j) {
		return i;
	}

	xa0 = a->x;
	xa = xa0 + j;
	xb0 = b->x;
	xb = xb0 + j;
	for (;;) {
		if (*--xa != *--xb) {
			return *xa < *xb ? -1 : 1;
		}

		if (xa <= xa0) {
			break;
		}
	}
	return 0;
}

static Bigint *diff(Bigint *a, Bigint *b)
{
	Bigint *c;
	int i, wa, wb;
	long borrow, y;				/* We need signed shifts here. */
	unsigned long *xa, *xae, *xb, *xbe, *xc;
#ifdef Pack_32
	int32_t z;
#endif

	i = cmp(a, b);
	if (!i) {
		c = Balloc(0);
		c->wds = 1;
		c->x[0] = 0;
		return c;
	}

	if (i < 0) {
		c = a;
		a = b;
		b = c;
		i = 1;
	} else {
		i = 0;
	}

	c = Balloc(a->k);
	c->sign = i;
	wa = a->wds;
	xa = a->x;
	xae = xa + wa;
	wb = b->wds;
	xb = b->x;
	xbe = xb + wb;
	xc = c->x;
	borrow = 0;
#ifdef Pack_32
	do {
		y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
		borrow = y >> 16;
		Sign_Extend(borrow, y);
		z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
		borrow = z >> 16;
		Sign_Extend(borrow, z);
		Storeinc(xc, z, y);
	} while (xb < xbe);

	while (xa < xae) {
		y = (*xa & 0xffff) + borrow;
		borrow = y >> 16;
		Sign_Extend(borrow, y);
		z = (*xa++ >> 16) + borrow;
		borrow = z >> 16;
		Sign_Extend(borrow, z);
		Storeinc(xc, z, y);
	}
#else
	do {
		y = *xa++ - *xb++ + borrow;
		borrow = y >> 16;
		Sign_Extend(borrow, y);
		*xc++ = y & 0xffff;
	} while (xb < xbe);

	while (xa < xae) {
		y = *xa++ + borrow;
		borrow = y >> 16;
		Sign_Extend(borrow, y);
		*xc++ = y & 0xffff;
	}
#endif

	while (!*--xc) {
		wa--;
	}

	c->wds = wa;
	return c;
}

static Bigint *d2b(double d, int *e, int *bits)
{
	Bigint *b;
	int de, i, k;
	unsigned long *x, y, z;

#ifdef Pack_32
	b = Balloc(1);
#else
	b = Balloc(2);
#endif
	x = b->x;

	z = word0(d) & Frac_mask;
	word0(d) &= 0x7fffffff;		/* clear sign bit, which we ignore */
	if ((de = (int)(word0(d) >> Exp_shift))) {
		z |= Exp_msk1;
	}
#ifdef Pack_32
	if ((y = word1(d))) {
		if ((k = lo0bits(&y))) {
			x[0] = y | z << (32 - k);
			z >>= k;
		} else {
			x[0] = y;
		}

		i = b->wds = (x[1] = z) ? 2 : 1;
	} else {
#ifdef CONFIG_DEBUG_LIB
		if (!z) {
			ldbg("Zero passed to d2b\n");
		}
#endif
		k = lo0bits(&z);
		x[0] = z;
		i = b->wds = 1;
		k += 32;
	}
#else
	if ((y = word1(d))) {
		if ((k = lo0bits(&y)))
			if (k >= 16) {
				x[0] = y | ((z << (32 - k)) & 0xffff);
				x[1] = z >> (k - 16) & 0xffff;
				x[2] = z >> k;
				i = 2;
			} else {
				x[0] = y & 0xffff;
				x[1] = (y >> 16) | ((z << (16 - k)) & 0xffff);
				x[2] = z >> k & 0xffff;
				x[3] = z >> (k + 16);
				i = 3;
			}
		else {
			x[0] = y & 0xffff;
			x[1] = y >> 16;
			x[2] = z & 0xffff;
			x[3] = z >> 16;
			i = 3;
		}
	} else {
#ifdef CONFIG_DEBUG_LIB
		if (!z) {
			ldbg("Zero passed to d2b\n");
		}
#endif
		k = lo0bits(&z);
		if (k >= 16) {
			x[0] = z;
			i = 0;
		} else {
			x[0] = z & 0xffff;
			x[1] = z >> 16;
			i = 1;
		}

		k += 32;
	}
	while (!x[i]) {
		--i;
	}
	b->wds = i + 1;
#endif
	if (de) {
		*e = de - Bias - (P - 1) + k;
		*bits = P - k;
	} else {
		*e = de - Bias - (P - 1) + 1 + k;
#ifdef Pack_32
		*bits = 32 * i - hi0bits(x[i - 1]);
#else
		*bits = (i + 2) * 16 - hi0bits(x[i]);
#endif
	}

	return b;
}

static const double tens[] = {
	1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
	1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
	1e20, 1e21, 1e22
};

#ifdef IEEE_Arith
static const double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };

#define n_bigtens 5
#else
static const double bigtens[] = { 1e16, 1e32 };
static const double tinytens[] = { 1e-16, 1e-32 };

#define n_bigtens 2
#endif

static int quorem(Bigint *b, Bigint *S)
{
	int n;
	long borrow, y;
	unsigned long carry, q, ys;
	unsigned long *bx, *bxe, *sx, *sxe;
#ifdef Pack_32
	int32_t z;
	uint32_t si, zs;
#endif

	n = S->wds;
#ifdef CONFIG_DEBUG_LIB
	if (b->wds > n) {
		ldbg("oversize b in quorem\n");
	}
#endif
	if (b->wds < n) {
		return 0;
	}

	sx = S->x;
	sxe = sx + --n;
	bx = b->x;
	bxe = bx + n;
	q = *bxe / (*sxe + 1);		/* ensure q <= true quotient */
#ifdef CONFIG_DEBUG_LIB
	if (q > 9) {
		ldbg("oversized quotient in quorem\n");
	}
#endif

	if (q) {
		borrow = 0;
		carry = 0;
		do {
#ifdef Pack_32
			si = *sx++;
			ys = (si & 0xffff) * q + carry;
			zs = (si >> 16) * q + (ys >> 16);
			carry = zs >> 16;
			y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
			borrow = y >> 16;
			Sign_Extend(borrow, y);
			z = (*bx >> 16) - (zs & 0xffff) + borrow;
			borrow = z >> 16;
			Sign_Extend(borrow, z);
			Storeinc(bx, z, y);
#else
			ys = *sx++ * q + carry;
			carry = ys >> 16;
			y = *bx - (ys & 0xffff) + borrow;
			borrow = y >> 16;
			Sign_Extend(borrow, y);
			*bx++ = y & 0xffff;
#endif
		} while (sx <= sxe);

		if (!*bxe) {
			bx = b->x;
			while (--bxe > bx && !*bxe) {
				--n;
			}

			b->wds = n;
		}
	}
	if (cmp(b, S) >= 0) {
		q++;
		borrow = 0;
		carry = 0;
		bx = b->x;
		sx = S->x;
		do {
#ifdef Pack_32
			si = *sx++;
			ys = (si & 0xffff) + carry;
			zs = (si >> 16) + (ys >> 16);
			carry = zs >> 16;
			y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
			borrow = y >> 16;
			Sign_Extend(borrow, y);
			z = (*bx >> 16) - (zs & 0xffff) + borrow;
			borrow = z >> 16;
			Sign_Extend(borrow, z);
			Storeinc(bx, z, y);
#else
			ys = *sx++ + carry;
			carry = ys >> 16;
			y = *bx - (ys & 0xffff) + borrow;
			borrow = y >> 16;
			Sign_Extend(borrow, y);
			*bx++ = y & 0xffff;
#endif
		} while (sx <= sxe);
		bx = b->x;
		bxe = bx + n;
		if (!*bxe) {
			while (--bxe > bx && !*bxe) {
				--n;
			}
			b->wds = n;
		}
	}

	return q;
}

/****************************************************************************
 * Public Functions
 ****************************************************************************/

/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
 *
 * Inspired by "How to Print Floating-Point Numbers Accurately" by
 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
 *
 * Modifications:
 *      1. Rather than iterating, we use a simple numeric overestimate
 *         to determine k = floor(log10(d)).  We scale relevant
 *         quantities using O(log2(k)) rather than O(k) multiplications.
 *      2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
 *         try to generate digits strictly left to right.  Instead, we
 *         compute with fewer bits and propagate the carry if necessary
 *         when rounding the final digit up.  This is often faster.
 *      3. Under the assumption that input will be rounded nearest,
 *         mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
 *         That is, we allow equality in stopping tests when the
 *         round-nearest rule will give the same floating-point value
 *         as would satisfaction of the stopping test with strict
 *         inequality.
 *      4. We remove common factors of powers of 2 from relevant
 *         quantities.
 *      5. When converting floating-point integers less than 1e16,
 *         we use floating-point arithmetic rather than resorting
 *         to multiple-precision integers.
 *      6. When asked to produce fewer than 15 digits, we first try
 *         to get by with floating-point arithmetic; we resort to
 *         multiple-precision integer arithmetic only if we cannot
 *         guarantee that the floating-point calculation has given
 *         the correctly rounded result.  For k requested digits and
 *         "uniformly" distributed input, the probability is
 *         something like 10^(k-15) that we must resort to the int32_t
 *         calculation.
 */

char *__dtoa(double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
{
	/* Arguments ndigits, decpt, sign are similar to those of ecvt and fcvt;
	 * trailing zeros are suppressed from the returned string.  If not null, *rve
	 * is set to point to the end of the return value.  If d is +-Infinity or
	 * NaN, then *decpt is set to 9999.
	 *
	 * mode: 0 ==> shortest string that yields d when read in and rounded to
	 * nearest. 1 ==> like 0, but with Steele & White stopping rule; e.g. with
	 * IEEE P754 arithmetic , mode 0 gives 1e23 whereas mode 1 gives
	 * 9.999999999999999e22. 2 ==> max(1,ndigits) significant digits.  This gives
	 * a return value similar to that of ecvt, except that trailing zeros are
	 * suppressed. 3 ==> through ndigits past the decimal point.  This gives a
	 * return value similar to that from fcvt, except that trailing zeros are
	 * suppressed, and ndigits can be negative. 4-9 should give the same return
	 * values as 2-3, i.e., 4 <= mode <= 9 ==> same return as mode 2 + (mode &
	 * 1).  These modes are mainly for debugging; often they run slower but
	 * sometimes faster than modes 2-3. 4,5,8,9 ==> left-to-right digit
	 * generation. 6-9 ==> don't try fast floating-point estimate (if
	 * applicable).
	 *
	 * Values of mode other than 0-9 are treated as mode 0.
	 *
	 * Sufficient space is allocated to the return value to hold the suppressed
	 * trailing zeros. */

	int bbits;
	int b2;
	int b5;
	int be;
	int dig;
	int i;
	int ieps;
	int ilim = 0;
	int ilim0;
	int ilim1 = 0;
	int j;
	int j_1;
	int k;
	int k0;
	int k_check;
	int leftright;
	int m2;
	int m5;
	int s2;
	int s5;
	int spec_case = 0;
	int try_quick;
	long L;
	int denorm;
	unsigned long x;
	Bigint *b;
	Bigint *b1;
	Bigint *delta;
	Bigint *mlo = NULL;
	Bigint *mhi;
	Bigint *S;
	double d2;
	double ds;
	double eps;
	char *s;
	char *s0;
	static Bigint *result;
	static int result_k;

	if (result) {
		result->k = result_k;
		result->maxwds = 1 << result_k;
		Bfree(result);
		result = 0;
	}

	if (word0(d) & Sign_bit) {
		/* set sign for everything, including 0's and NaNs */
		*sign = 1;
		word0(d) &= ~Sign_bit;	/* clear sign bit */
	} else {
		*sign = 0;
	}

#if defined(IEEE_Arith)
#ifdef IEEE_Arith
	if ((word0(d) & Exp_mask) == Exp_mask)
#else
	if (word0(d) == 0x8000)
#endif
	{
		/* Infinity or NaN */
		*decpt = 9999;
		s =
#ifdef IEEE_Arith
			!word1(d) && !(word0(d) & 0xfffff) ? "Infinity" :
#endif
			"NaN";
		if (rve) {
			*rve =
#ifdef IEEE_Arith
				s[3] ? s + 8 :
#endif
				s + 3;
		}

		return s;
	}
#endif
	if (!d) {
		*decpt = 1;
		s = "0";
		if (rve) {
			*rve = s + 1;
		}

		return s;
	}

	b = d2b(d, &be, &bbits);
	if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask >> Exp_shift1)))) {
		d2 = d;
		word0(d2) &= Frac_mask1;
		word0(d2) |= Exp_11;

		/* log(x) ~=~ log(1.5) + (x-1.5)/1.5 log10(x) = log(x) / log(10) ~=~
		 * log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) log10(d) =
		 * (i-Bias)*log(2)/log(10) + log10(d2) This suggests computing an
		 * approximation k to log10(d) by k = (i - Bias)*0.301029995663981 + (
		 * (d2-1.5)*0.289529654602168 + 0.176091259055681 ); We want k to be too
		 * large rather than too small. The error in the first-order Taylor
		 * series approximation is in our favor, so we just round up the constant
		 * enough to compensate for any error in the multiplication of (i - Bias)
		 * by 0.301029995663981; since |i - Bias| <= 1077, and 1077 * 0.30103 *
		 * 2^-52 ~=~ 7.2e-14, adding 1e-13 to the constant term more than
		 * suffices. Hence we adjust the constant term to 0.1760912590558. (We
		 * could get a more accurate k by invoking log10, but this is probably
		 * not worthwhile.) */

		i -= Bias;
		denorm = 0;
	} else {
		/* d is denormalized */

		i = bbits + be + (Bias + (P - 1) - 1);
		x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
			: word1(d) << (32 - i);
		d2 = x;
		word0(d2) -= 31 * Exp_msk1;	/* adjust exponent */
		i -= (Bias + (P - 1) - 1) + 1;
		denorm = 1;
	}

	ds = (d2 - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
	k = (int)ds;
	if (ds < 0. && ds != k) {
		k--;					/* want k = floor(ds) */
	}

	k_check = 1;

	if (k >= 0 && k <= Ten_pmax) {
		if (d < tens[k]) {
			k--;
		}
		k_check = 0;
	}

	j = bbits - i - 1;
	if (j >= 0) {
		b2 = 0;
		s2 = j;
	} else {
		b2 = -j;
		s2 = 0;
	}

	if (k >= 0) {
		b5 = 0;
		s5 = k;
		s2 += k;
	} else {
		b2 -= k;
		b5 = -k;
		s5 = 0;
	}

	if (mode < 0 || mode > 9) {
		mode = 0;
	}

	try_quick = 1;
	if (mode > 5) {
		mode -= 4;
		try_quick = 0;
	}

	leftright = 1;
	switch (mode) {
	case 0:
	case 1:
		ilim = ilim1 = -1;
		i = 18;
		ndigits = 0;
		break;

	case 2:
		leftright = 0;
	/* no break */
	case 4:
		if (ndigits <= 0) {
			ndigits = 1;
		}

		ilim = ilim1 = i = ndigits;
		break;

	case 3:
		leftright = 0;
	/* no break */
	case 5:
		i = ndigits + k + 1;
		ilim = i;
		ilim1 = i - 1;
		if (i <= 0) {
			i = 1;
		}
	}

	j = sizeof(unsigned long);
	for (result_k = 0; (signed)(sizeof(Bigint) - sizeof(unsigned long) + j) <= i; j <<= 1) {
		result_k++;
	}

	result = Balloc(result_k);
	s = s0 = (char *)result;

	if (ilim >= 0 && ilim <= Quick_max && try_quick) {
		/* Try to get by with floating-point arithmetic. */

		i = 0;
		d2 = d;
		k0 = k;
		ilim0 = ilim;
		ieps = 2;				/* conservative */

		if (k > 0) {
			ds = tens[k & 0xf];
			j = k >> 4;

			if (j & Bletch) {
				/* prevent overflows */
				j &= Bletch - 1;
				d /= bigtens[n_bigtens - 1];
				ieps++;
			}

			for (; j; j >>= 1, i++) {
				if (j & 1) {
					ieps++;
					ds *= bigtens[i];
				}
			}

			d /= ds;
		} else if ((j_1 = -k)) {
			d *= tens[j_1 & 0xf];
			for (j = j_1 >> 4; j; j >>= 1, i++) {
				if (j & 1) {
					ieps++;
					d *= bigtens[i];
				}
			}
		}

		if (k_check && d < 1. && ilim > 0) {
			if (ilim1 <= 0) {
				goto fast_failed;
			}

			ilim = ilim1;
			k--;
			d *= 10.;
			ieps++;
		}

		eps = ieps * d + 7.;
		word0(eps) -= (P - 1) * Exp_msk1;
		if (ilim == 0) {
			S = mhi = 0;
			d -= 5.;
			if (d > eps) {
				goto one_digit;
			}
			if (d < -eps) {
				goto no_digits;
			}
			goto fast_failed;
		}
#ifndef No_leftright
		if (leftright) {
			/* Use Steele & White method of only generating digits needed. */

			eps = 0.5 / tens[ilim - 1] - eps;
			for (i = 0;;) {
				L = (int)d;
				d -= L;
				*s++ = '0' + (int)L;
				if (d < eps) {
					goto ret1;
				}

				if (1. - d < eps) {
					goto bump_up;
				}

				if (++i >= ilim) {
					break;
				}

				eps *= 10.;
				d *= 10.;
			}
		} else {
#endif
			/* Generate ilim digits, then fix them up. */

			eps *= tens[ilim - 1];
			for (i = 1;; i++, d *= 10.) {
				L = (int)d;
				d -= L;
				*s++ = '0' + (int)L;
				if (i == ilim) {
					if (d > 0.5 + eps) {
						goto bump_up;
					} else if (d < 0.5 - eps) {
						while (*--s == '0');
						s++;
						goto ret1;
					}

					break;
				}
			}
#ifndef No_leftright
		}
#endif
fast_failed:
		s = s0;
		d = d2;
		k = k0;
		ilim = ilim0;
	}

	/* Do we have a "small" integer? */

	if (be >= 0 && k <= Int_max) {
		/* Yes. */

		ds = tens[k];
		if (ndigits < 0 && ilim <= 0) {
			S = mhi = 0;
			if (ilim < 0 || d <= 5 * ds) {
				goto no_digits;
			}

			goto one_digit;
		}

		for (i = 1;; i++) {
			L = (int)(d / ds);
			d -= L * ds;
#ifdef Check_FLT_ROUNDS
			/* If FLT_ROUNDS == 2, L will usually be high by 1 */
			if (d < 0) {
				L--;
				d += ds;
			}
#endif
			*s++ = '0' + (int)L;
			if (i == ilim) {
				d += d;
				if (d > ds || (d == ds && (L & 1))) {
bump_up:
					while (*--s == '9')
						if (s == s0) {
							k++;
							*s = '0';
							break;
						}

					++*s++;
				}
				break;
			}

			if (!(d *= 10.)) {
				break;
			}
		}

		goto ret1;
	}

	m2 = b2;
	m5 = b5;
	mhi = mlo = 0;
	if (leftright) {
		if (mode < 2) {
			i = denorm ? be + (Bias + (P - 1) - 1 + 1) : 1 + P - bbits;
		} else {
			j = ilim - 1;
			if (m5 >= j) {
				m5 -= j;
			} else {
				s5 += j -= m5;
				b5 += j;
				m5 = 0;
			}

			if ((i = ilim) < 0) {
				m2 -= i;
				i = 0;
			}
		}

		b2 += i;
		s2 += i;
		mhi = i2b(1);
	}

	if (m2 > 0 && s2 > 0) {
		i = m2 < s2 ? m2 : s2;
		b2 -= i;
		m2 -= i;
		s2 -= i;
	}

	if (b5 > 0) {
		if (leftright) {
			if (m5 > 0) {
				mhi = pow5mult(mhi, m5);
				b1 = mult(mhi, b);
				Bfree(b);
				b = b1;
			}

			if ((j = b5 - m5)) {
				b = pow5mult(b, j);
			}
		} else {
			b = pow5mult(b, b5);
		}
	}

	S = i2b(1);
	if (s5 > 0) {
		S = pow5mult(S, s5);
	}

	/* Check for special case that d is a normalized power of 2. */

	if (mode < 2) {
		if (!word1(d) && !(word0(d) & Bndry_mask) && word0(d) & Exp_mask) {
			/* The special case */
			b2 += Log2P;
			s2 += Log2P;
			spec_case = 1;
		} else {
			spec_case = 0;
		}
	}

	/* Arrange for convenient computation of quotients: shift left if
	 * necessary so divisor has 4 leading 0 bits.
	 *
	 * Perhaps we should just compute leading 28 bits of S once and for all
	 * and pass them and a shift to quorem, so it can do shifts and ors
	 * to compute the numerator for q.
	 */

#ifdef Pack_32
	if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds - 1]) : 1) + s2) & 0x1f)) {
		i = 32 - i;
	}
#else
	if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds - 1]) : 1) + s2) & 0xf)) {
		i = 16 - i;
	}
#endif

	if (i > 4) {
		i -= 4;
		b2 += i;
		m2 += i;
		s2 += i;
	} else if (i < 4) {
		i += 28;
		b2 += i;
		m2 += i;
		s2 += i;
	}

	if (b2 > 0) {
		b = lshift(b, b2);
	}

	if (s2 > 0) {
		S = lshift(S, s2);
	}

	if (k_check) {
		if (cmp(b, S) < 0) {
			k--;
			b = multadd(b, 10, 0);	/* we botched the k estimate */
			if (leftright) {
				mhi = multadd(mhi, 10, 0);
			}

			ilim = ilim1;
		}
	}

	if (ilim <= 0 && mode > 2) {
		if (ilim < 0 || cmp(b, S = multadd(S, 5, 0)) <= 0) {
			/* no digits, fcvt style */

no_digits:
			k = -1 - ndigits;
			goto ret;
		}

one_digit:
		*s++ = '1';
		k++;
		goto ret;
	}

	if (leftright) {
		if (m2 > 0) {
			mhi = lshift(mhi, m2);
		}

		/* Compute mlo -- check for special case that d is a normalized power of
		 * 2. */

		mlo = mhi;
		if (spec_case) {
			mhi = Balloc(mhi->k);
			Bcopy(mhi, mlo);
			mhi = lshift(mhi, Log2P);
		}

		for (i = 1;; i++) {
			dig = quorem(b, S) + '0';
			/* Do we yet have the shortest decimal string that will round to d? */
			j = cmp(b, mlo);
			delta = diff(S, mhi);
			j_1 = delta->sign ? 1 : cmp(b, delta);
			Bfree(delta);
#ifndef ROUND_BIASED
			if (j_1 == 0 && !mode && !(word1(d) & 1)) {
				if (dig == '9') {
					goto round_9_up;
				}

				if (j > 0) {
					dig++;
				}

				*s++ = dig;
				goto ret;
			}
#endif
			if (j < 0 || (j == 0 && !mode
#ifndef ROUND_BIASED
						  && (!(word1(d) & 1))
#endif
						 )) {
				if ((j_1 > 0)) {
					b = lshift(b, 1);
					j_1 = cmp(b, S);
					if ((j_1 > 0 || (j_1 == 0 && (dig & 1))) && dig++ == '9') {
						goto round_9_up;
					}
				}

				*s++ = dig;
				goto ret;
			}

			if (j_1 > 0) {
				if (dig == '9') {
					/* possible if i == 1 */
round_9_up:
					*s++ = '9';
					goto roundoff;
				}

				*s++ = dig + 1;
				goto ret;
			}

			*s++ = dig;
			if (i == ilim) {
				break;
			}

			b = multadd(b, 10, 0);
			if (mlo == mhi) {
				mlo = mhi = multadd(mhi, 10, 0);
			} else {
				mlo = multadd(mlo, 10, 0);
				mhi = multadd(mhi, 10, 0);
			}
		}
	} else {
		for (i = 1;; i++) {
			*s++ = dig = quorem(b, S) + '0';
			if (i >= ilim) {
				break;
			}

			b = multadd(b, 10, 0);
		}
	}

	/* Round off last digit */

	b = lshift(b, 1);
	j = cmp(b, S);
	if (j > 0 || (j == 0 && (dig & 1))) {
roundoff:
		while (*--s == '9')
			if (s == s0) {
				k++;
				*s++ = '1';
				goto ret;
			}

		++*s++;
	} else {
		while (*--s == '0') ;
		s++;
	}

ret:
	Bfree(S);
	if (mhi) {
		if (mlo && mlo != mhi) {
			Bfree(mlo);
		}

		Bfree(mhi);
	}
ret1:
	Bfree(b);
	if (s == s0) {
		/* Don't return empty string */
		*s++ = '0';
		k = 0;
	}

	*s = 0;
	*decpt = k + 1;
	if (rve) {
		*rve = s;
	}

	return s0;
}
